Modeling and constrained control of transportation network

The linear modeling of urban transportation network provides a good approach to design traffic signal control strategies. However, the actual region of the model validity is always bounded, and hard constraints on state and control variables should be specified as a part and as a limitation of the model. This paper focuses on this issue and adapts the positive invariance approach of set to construct a constrained feedback controller subject to additive disturbances. In particular, a set of linear conditions is presented for the feedback gain that respects the constraints on both state and control. Finally, an example with four intersections is carried out in order to illustrate the results.